https://file.aiquickdraw.com/mathbot/file/1727117232650j7rpenow.jpg

The question in the image is:

"If the interest was to accumulate quarterly in arrears and 6.25% was the annual nominal rate, what difference would it make to the answer given?"

### Explanation:

The key points in the question:
- **Interest accumulates quarterly in arrears**: This means that interest is compounded four times a year (quarterly), and it's applied at the end of each period.
- **6.25% annual nominal rate**: The interest rate given is the annual rate, but with quarterly compounding, we need to adjust it for each period.

#### Steps to solve:

1. **Convert the annual nominal rate to a quarterly rate**:
   The nominal annual rate is 6.25%, so the quarterly rate would be:

   \[
   \text{Quarterly rate} = \frac{6.25\%}{4} = 1.5625\% \text{ per quarter}
   \]

2. **Impact of compounding quarterly**:
   When compounding quarterly, the **effective annual rate (EAR)** will be slightly higher than the nominal rate. We can calculate the EAR using the formula:

   \[
   \text{EAR} = \left(1 + \frac{r_{\text{nominal}}}{n}\right)^n - 1
   \]
   Where:
   - \( r_{\text{nominal}} = 0.0625 \) (annual nominal rate)
   - \( n = 4 \) (since compounding is quarterly)

   So:

   \[
   \text{EAR} = \left(1 + \frac{0.0625}{4}\right)^4 - 1
   \]

3. **What difference would it make?**
   If the interest accumulates quarterly, the final amount (or value) after interest would increase because of the compounding effect. The exact difference would depend on the original principal and the time period over which the interest is being calculated.

Would you like me to calculate the exact difference, or do you have further questions? 

### Related Questions:
1. What is the formula to calculate interest compounded quarterly?
2. How does the effective annual rate (EAR) differ from the nominal rate?
3. What would be the effective interest rate if the nominal rate was compounded monthly?
4. How does compounding frequency affect loan or investment returns?
5. What is the difference between interest compounded in arrears versus in advance?

### Tip:
The more frequent the compounding, the higher the effective interest rate becomes!

If the interest was to accumulate quarterly in arrears and 6.25% was the annual nominal rate, what difference would it make to the answer given?

Explore how interest compounding quarterly in arrears affects a 6.25% annual nominal rate. Learn the formulas and methods to calculate the quarterly rate and effective annual rate (EAR), and understand how compounding frequency impacts the final amount.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation